1. **State the problem:** We are given a triangle with angles $\alpha = 45^\circ$, $\gamma = 73^\circ$, and side $b = 240$ cm opposite angle $\beta$. We need to find angle $\beta$ and sides $a$ and $c$, rounding angles to the nearest degree and sides to the nearest centimeter. 2. **Find angle $\beta$:** The sum of angles in a triangle is $180^\circ$. So, $$\beta = 180^\circ - \alpha - \gamma = 180^\circ - 45^\circ - 73^\circ = 62^\circ.$$ 3. **Use Law of Sines to find sides $a$ and $c$:** The Law of Sines states $$\frac{a}{\sin \alpha} = \frac{b}{\sin \beta} = \frac{c}{\sin \gamma}.$$ Given $b=240$ cm and $\beta=62^\circ$, we find common ratio $$k = \frac{b}{\sin \beta} = \frac{240}{\sin 62^\circ}.$$ Calculate $\sin 62^\circ \approx 0.8829$, so $$k \approx \frac{240}{0.8829} \approx 271.84.$$ 4. **Calculate side $a$:** $$a = k \times \sin \alpha = 271.84 \times \sin 45^\circ.$$ $\sin 45^\circ = \frac{\sqrt{2}}{2} \approx 0.7071$, so $$a \approx 271.84 \times 0.7071 = 192.12.$$ Rounded to nearest cm, $a = 192$ cm. 5. **Calculate side $c$:** $$c = k \times \sin \gamma = 271.84 \times \sin 73^\circ.$$ $\sin 73^\circ \approx 0.9563$, so $$c \approx 271.84 \times 0.9563 = 259.89.$$ Rounded to nearest cm, $c = 260$ cm. **Final answers:** - $\beta = 62^\circ$ - $a = 192$ cm - $c = 260$ cm